The conductivity of a pure semiconductor is roughly proportional to `T^(3/2) e^(-Delta E//2kT)` where `(Delta)E` is the band gap. The band gap for germanium is 0.74eV at 4K and 0.67eV at 300K.By what factor does the conductivity of pure germanium increase as the temperature is raised form 4K to 300K?

Explanation

To solve the problem of how the conductivity of pure germanium increases when the temperature is raised from 4K to 300K, we will follow these steps:

### Step 1: Write the expression for conductivity
The conductivity (\(\sigma\)) of a pure semiconductor is given by the formula:
\[ \sigma \propto T^{3/2} e^{-\frac{\Delta E}{2kT}} \]
where:
...